Other stuff:
I present below some animations obtained in the same manner as a cartoon. We used the technique of simulation called distinct (or discrete) element method (DEM). This means that every grain is modeled separately. For the first five types of experience, we used the rigid-particle method to manage collisions.
Click here (1.5 Mb) or here (1.2 Mb) to see an animation of the convection induced by high amplitude and low frequency vertical vibrations. If we shake the box with low amplitude and high frequency vertical vibrations, the result is quite different (1.2 Mb).
Click here (1.2 Mb) to see an animation of the convection induced by horizontal vibrations.
Click here or here (1.2 Mb) to see an animation of the convection induced by vertical AND horizontal vibrations.
Click here (1.2 Mb) to see an animation of the convection induced by vertical vibrations. The vertical walls go up and down and induce a shear.
Click here (1.2 Mb) to see an animation of the convection induced by vertical vibrations. The vertical walls go up and down in the opposite direction of the previous simulation.
This simulation is the same as the first one, but with friction equal to 0. You will be convinced that friction has a great influence when looking at here (1.7 Mb). However, circular motions appear when vibrations are weak, as you can see here (1.1 Mb).
Click here (0.3 Mb) to see an animation.
In the experiment below, we compared four media composed. Curves depict the percentage of grains passed in terms of time. P means sharp-pointed aspect, R round aspect, e elastic (coefficient of restitution=0.9, coefficient of friction=0.1), r rugose (0.5, 0.5). Incline of walls is 30 degrees with respect to vertical.
Clearly "elastic" grains flow more quickly than rugose ones. Shape has no effect. On the other hand, the speed of flow does not depend on the number of grains still in the hopper : the flow is linear. "Flat" regions indicate temporary bottlenecks.
Click here (0.3 Mb) to see what happens when we turn the gravity vector on 45 degrees.
This method has several advantages. For example we can visualize forces between the grains, as you can see on this image (44 Ko).
The manner grains are arranged plays a pominent part in dissipation of energy, as we can see it on three examples : when the medium is amorphous (183 Ko), when all grains have the same size and are arranged in alternate rows (93 Ko) or arranged on a square mesh 188 (Ko).
